<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- This manual is for FFTW
(version 3.3.10, 10 December 2020).

Copyright (C) 2003 Matteo Frigo.

Copyright (C) 2003 Massachusetts Institute of Technology.

Permission is granted to make and distribute verbatim copies of this
manual provided the copyright notice and this permission notice are
preserved on all copies.

Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided that the
entire resulting derived work is distributed under the terms of a
permission notice identical to this one.

Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that this permission notice may be stated in a translation
approved by the Free Software Foundation. -->
<!-- Created by GNU Texinfo 6.7, http://www.gnu.org/software/texinfo/ -->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>Transposed distributions (FFTW 3.3.10)</title>

<meta name="description" content="Transposed distributions (FFTW 3.3.10)">
<meta name="keywords" content="Transposed distributions (FFTW 3.3.10)">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<link href="index.html" rel="start" title="Top">
<link href="Concept-Index.html" rel="index" title="Concept Index">
<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
<link href="MPI-Data-Distribution.html" rel="up" title="MPI Data Distribution">
<link href="One_002ddimensional-distributions.html" rel="next" title="One-dimensional distributions">
<link href="Load-balancing.html" rel="prev" title="Load balancing">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.indentedblock {margin-right: 0em}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
kbd {font-style: oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
span.nolinebreak {white-space: nowrap}
span.roman {font-family: initial; font-weight: normal}
span.sansserif {font-family: sans-serif; font-weight: normal}
ul.no-bullet {list-style: none}
-->
</style>


</head>

<body lang="en">
<span id="Transposed-distributions"></span><div class="header">
<p>
Next: <a href="One_002ddimensional-distributions.html" accesskey="n" rel="next">One-dimensional distributions</a>, Previous: <a href="Load-balancing.html" accesskey="p" rel="prev">Load balancing</a>, Up: <a href="MPI-Data-Distribution.html" accesskey="u" rel="up">MPI Data Distribution</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<span id="Transposed-distributions-1"></span><h4 class="subsection">6.4.3 Transposed distributions</h4>

<p>Internally, FFTW&rsquo;s MPI transform algorithms work by first computing
transforms of the data local to each process, then by globally
<em>transposing</em> the data in some fashion to redistribute the data
among the processes, transforming the new data local to each process,
and transposing back.  For example, a two-dimensional <code>n0</code> by
<code>n1</code> array, distributed across the <code>n0</code> dimension, is
transformd by: (i) transforming the <code>n1</code> dimension, which are
local to each process; (ii) transposing to an <code>n1</code> by <code>n0</code>
array, distributed across the <code>n1</code> dimension; (iii) transforming
the <code>n0</code> dimension, which is now local to each process; (iv)
transposing back.
<span id="index-transpose"></span>
</p>

<p>However, in many applications it is acceptable to compute a
multidimensional DFT whose results are produced in transposed order
(e.g., <code>n1</code> by <code>n0</code> in two dimensions).  This provides a
significant performance advantage, because it means that the final
transposition step can be omitted.  FFTW supports this optimization,
which you specify by passing the flag <code>FFTW_MPI_TRANSPOSED_OUT</code>
to the planner routines.  To compute the inverse transform of
transposed output, you specify <code>FFTW_MPI_TRANSPOSED_IN</code> to tell
it that the input is transposed.  In this section, we explain how to
interpret the output format of such a transform.
<span id="index-FFTW_005fMPI_005fTRANSPOSED_005fOUT"></span>
<span id="index-FFTW_005fMPI_005fTRANSPOSED_005fIN"></span>
</p>

<p>Suppose you have are transforming multi-dimensional data with (at
least two) dimensions n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;n<sub>d-1</sub>
.  As always, it is distributed along
the first dimension n<sub>0</sub>
.  Now, if we compute its DFT with the
<code>FFTW_MPI_TRANSPOSED_OUT</code> flag, the resulting output data are stored
with the first <em>two</em> dimensions transposed: n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&hellip;&times;&nbsp;n<sub>d-1</sub>
,
distributed along the n<sub>1</sub>
 dimension.  Conversely, if we take the
n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&hellip;&times;&nbsp;n<sub>d-1</sub>
 data and transform it with the
<code>FFTW_MPI_TRANSPOSED_IN</code> flag, then the format goes back to the
original n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;n<sub>d-1</sub>
 array.
</p>
<p>There are two ways to find the portion of the transposed array that
resides on the current process.  First, you can simply call the
appropriate &lsquo;<samp>local_size</samp>&rsquo; function, passing n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&hellip;&times;&nbsp;n<sub>d-1</sub>
 (the
transposed dimensions).  This would mean calling the &lsquo;<samp>local_size</samp>&rsquo;
function twice, once for the transposed and once for the
non-transposed dimensions.  Alternatively, you can call one of the
&lsquo;<samp>local_size_transposed</samp>&rsquo; functions, which returns both the
non-transposed and transposed data distribution from a single call.
For example, for a 3d transform with transposed output (or input), you
might call:
</p>
<div class="example">
<pre class="example">ptrdiff_t fftw_mpi_local_size_3d_transposed(
                ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2, MPI_Comm comm,
                ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
                ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
</pre></div>
<span id="index-fftw_005fmpi_005flocal_005fsize_005f3d_005ftransposed"></span>

<p>Here, <code>local_n0</code> and <code>local_0_start</code> give the size and
starting index of the <code>n0</code> dimension for the
<em>non</em>-transposed data, as in the previous sections.  For
<em>transposed</em> data (e.g. the output for
<code>FFTW_MPI_TRANSPOSED_OUT</code>), <code>local_n1</code> and
<code>local_1_start</code> give the size and starting index of the <code>n1</code>
dimension, which is the first dimension of the transposed data
(<code>n1</code> by <code>n0</code> by <code>n2</code>).
</p>
<p>(Note that <code>FFTW_MPI_TRANSPOSED_IN</code> is completely equivalent to
performing <code>FFTW_MPI_TRANSPOSED_OUT</code> and passing the first two
dimensions to the planner in reverse order, or vice versa.  If you
pass <em>both</em> the <code>FFTW_MPI_TRANSPOSED_IN</code> and
<code>FFTW_MPI_TRANSPOSED_OUT</code> flags, it is equivalent to swapping the
first two dimensions passed to the planner and passing <em>neither</em>
flag.)
</p>
<hr>
<div class="header">
<p>
Next: <a href="One_002ddimensional-distributions.html" accesskey="n" rel="next">One-dimensional distributions</a>, Previous: <a href="Load-balancing.html" accesskey="p" rel="prev">Load balancing</a>, Up: <a href="MPI-Data-Distribution.html" accesskey="u" rel="up">MPI Data Distribution</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
</div>



</body>
</html>
